A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in R^N

We derive a Pohoaev-Trudinger type embedding for the Lorentz-Sobolev space W1"0LN,q(Ω), for general domains Ω⊆RN and in particular for Ω=RN. Precisely, we first prove that the corresponding inequality is domain independent and then, by constructing explicit concentrating sequences à la Moser, we establish that the embedding inequality is sharp and we exhibit the best constant.